Derivation of the Plane Stress Problem
Purpose of Lesson To derive the governing differential equations and associated boundary conditions for the two-dimensional plane stress problem by applying the principle of minimum potential energy and the techniques of variational calculus to the potential energy functional.
We first form an expression for the potential energy as a function of the two independent displacements, u and v. This defines the functional form that must be minimized. We then use the calculus of variations to identify the conditions necessary to minimize a functional in two dimensions. As was the case in one dimension, the conditions that must be satisfied are the Euler-Lagrange equations and the boundary terms. When ...
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